Bah! sidewaystable va bene, ma di solito richiede che si impostino un certo numero di parametri, anche per evitare che nelle pagine di sinistra la tabella sia ruotata in verso orario. Gli oggetti in landscape vanno sempre ruotati in verso antiorario; con \rotatebox è più semplice e diretto.
Comunque osserva che anche con \rotatebox la tabella girata esce dei margini.
Te ne mando un’altra piccola variazione, dove osserverai che ho tolto tutti gli \hline, sostituendoli con i comandi corretti del pacchetto booktabs; ho eliminato le colonne espandibili X eliminando anche la `x’ da tabularx e la specificazione della sua larghezza, ho usato correttamente il ripetitore di colonna (*{11}l). Ora ogni colonna ha la sua larghezza naturale. Ho aggiunto un minimo di spazio fra la didascalia e la tabella.
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\documentclass{book}
\usepackage{tabularx,array,booktabs,graphicx}
\begin{document}
\begin{table}[p]\footnotesize\center
\rotatebox{90}{%
\begin{minipage}{\textheight}
\caption{Regression with robust se lagged vars and avg5 vars year fe}\vspace{1ex}
\begin{tabular}{*{11}l}
\toprule
&\multicolumn{1}{c}{(1)} &\multicolumn{1}{c}{(2)} &\multicolumn{1}{c}{(3)} &\multicolumn{1}{c}{(4)} &\multicolumn{1}{c}{(5)} &\multicolumn{1}{c}{(6)} &\multicolumn{1}{c}{(7)} &\multicolumn{1}{c}{(Cool} &\multicolumn{1}{c}{(9)} &\multicolumn{1}{c}{(10)} \\
\midrule
lagpolity1 & 0.014***& & 0.054***& &0.112*** & &0.031*** & &0.047*** & \\
& (0.000) & & (0.002) & &(0.007) & &(0.001) & &(0.002) & \\
lagpolity2 & 0.027***& & 0.123***& &0.347*** & &0.069*** & &0.103*** & \\
& (0.001) & & (0.002) & &(0.007) & &(0.001) & &(0.002) & \\
avg5polity1 & & 0.015***& &0.045*** & &0.116*** & &0.026*** & &0.040*** \\
& & (0.001) & &(0.002) & &(0.007) & &(0.001) & &(0.002) \\
avg5polity2 & & 0.028***& &0.114*** & &0.352*** & &0.065*** & &0.090*** \\
& & (0.001) & &(0.002) & &(0.008) & &(0.001) & &(0.003) \\
lngdp1 & 0.926***& 0.932***& 0.922***& 0.930***& 0.911***& 0.918***& 0.922***& 0.931***& 0.945***& 0.952***\\
& (0.002) & (0.002) & (0.002) & (0.002) & (0.002) & (0.002) & (0.002) & (0.002) & (0.002) & (0.002) \\
lngdp2 & 1.022***& 1.033***& 1.051***& 1.090***& 1.023***& 1.037***& 1.054***& 1.092***& 1.063***& 1.105***\\
& (0.002) & (0.002) & (0.002) & (0.002) & (0.002) & (0.002) & (0.002) & (0.002) & (0.002) & (0.002) \\
landl & -0.313***& -0.322***& -0.380***& -0.438***& -0.349***& -0.357***& -0.381***& -0.437***& -0.350***& -0.409***\\
& (0.008) & (0.008) & (0.008) & (0.009) & (0.007) & (0.007) & (0.008) & (0.009) & (0.009) & (0.010) \\
lndistw & -1.065***& -1.084***& -1.187***& -1.226***& -1.098***& -1.115***& -1.192***& -1.231***& -1.150***& -1.190***\\
& (0.004) & (0.004) & (0.005) & (0.005) & (0.004) & (0.004) & (0.005) & (0.005) & (0.005) & (0.006) \\
comlang & 0.332***& 0.354***& 0.436***& 0.455***& 0.390***& 0.409***& 0.451***& 0.468***& 0.388***& 0.404***\\
& (0.009) & (0.009) & (0.010) & (0.011) & (0.009) & (0.009) & (0.010) & (0.011) & (0.011) & (0.012) \\
border & 0.509***& 0.497***& 0.546***& 0.638***& 0.367***& 0.368***& 0.527***& 0.620***& 0.677***& 0.772***\\
& (0.018) & (0.019) & (0.021) & (0.024) & (0.018) & (0.019) & (0.021) & (0.024) & (0.021) & (0.025) \\
colony & 0.222***& 0.230***& 0.339***& 0.292***& 0.282***& 0.289***& 0.327***& 0.279***& 0.282***& 0.230***\\
& (0.019) & (0.019) & (0.022) & (0.025) & (0.018) & (0.019) & (0.022) & (0.025) & (0.022) & (0.025) \\
comcol & 0.727***& 0.695***& 0.768***& 0.812***& 0.706***& 0.681***& 0.765***& 0.812***& 0.797***& 0.846***\\
& (0.016) & (0.017) & (0.016) & (0.018) & (0.015) & (0.016) & (0.016) & (0.018) & (0.018) & (0.020) \\
col45 & 1.465***& 1.417***& 1.390***& 1.370***& 1.527***& 1.476***& 1.400***& 1.381***& 1.328***& 1.309***\\
& (0.026) & (0.027) & (0.029) & (0.034) & (0.025) & (0.026) & (0.029) & (0.034) & (0.031) & (0.035) \\
samectry & 0.365***& 0.417***& 0.473***& 0.496***& 0.485***& 0.529***& 0.470***& 0.492***& 0.309***& 0.306***\\
& (0.028) & (0.030) & (0.032) & (0.037) & (0.028) & (0.029) & (0.032) & (0.037) & (0.034) & (0.039) \\
rta & 0.216***& 0.191***& 0.249***& 0.226***& 0.290***& 0.268***& 0.237***& 0.214***& 0.162***& 0.139***\\
& (0.009) & (0.009) & (0.009) & (0.009) & (0.008) & (0.008) & (0.009) & (0.009) & (0.009) & (0.010) \\
comcur & 0.255***& 0.246***& 0.157***& 0.094***& 0.354***& 0.322***& 0.166***& 0.103***& -0.007 & -0.058 \\
& (0.028) & (0.030) & (0.032) & (0.035) & (0.027) & (0.028) & (0.032) & (0.035) & (0.034) & (0.037) \\
comleg & 0.209***& 0.182***& 0.199***& 0.166***& 0.196***& 0.174***& 0.196***& 0.162***& 0.198***& 0.162***\\
& (0.008) & (0.008) & (0.008) & (0.009) & (0.007) & (0.008) & (0.008) & (0.009) & (0.009) & (0.010) \\
gatt & 0.093***& 0.072***& 0.012 & 0.000 & 0.107***& 0.100***& 0.020** & 0.009 & 0.065***& 0.051***\\
& (0.007) & (0.008) & (0.008) & (0.009) & (0.007) & (0.007) & (0.008) & (0.009) & (0.008) & (0.010) \\
\midrule
R2 & 0.635 & 0.640 & 0.645 & 0.651 & 0.641 & 0.644 & 0.645 & 0.650 & 0.641 & 0.649 \\
N & 444899 & 416324 & 414969 & 330380 & 507858 & 476870 & 414969 & 330380 & 354601 & 277959 \\
\bottomrule
\end{tabular}\end{minipage}}
\end{table}
\end{document}
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